Theorems · Definition · algebraic topology
Path.Homotopic.Quotient.cast
{X : Type u} →
[inst : TopologicalSpace X] →
{x y : X} → Path.Homotopic.Quotient x y → {x' y' : X} → x' = x → y' = y → Path.Homotopic.Quotient x' y'Cast a path homotopy class using equalities of endpoints.
- Defined in
- Mathlib.Topology.Homotopy.Path
- Cited by
- 16 results in Mathlib
- Foundations
- Depth 132 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- TopologicalSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- TopologicalSpacestatement and proof · cited by 24,529
- Pathproof · cited by 318
- Path.Homotopic.Quotientstatement and proof · cited by 55
- Path.castproof · cited by 22
- Quotient.mapproof · cited by 7
Cited by16
Results whose statement or proof uses this declaration.
- IsQuotientCoveringMap.monodromy_toPermFiberproof · cited by 3
- Path.Homotopic.Quotient.cast_rfl_rflstatement and proof · cited by 3
- IsCoveringMap.monodromy_eq_of_map_eqstatement and proof · cited by 3
- FundamentalGroup.mapOfEq_applystatement · cited by 2
- IsCoveringMap.map_liftPathQuotientstatement · cited by 2
- FundamentalGroupoid.conj_eqToHomstatement · cited by 2
- IsQuotientCoveringMap.ker_monodromyPermproof · cited by 2
- Path.Homotopic.Quotient.cast_caststatement and proof · cited by 1
- Path.Homotopic.Quotient.cast_heqstatement · cited by 1
- Path.Homotopic.Quotient.map_caststatement and proof · cited by 1
- Path.Homotopic.Quotient.cast.congr_simpstatement and proof · cited by 1
- IsCoveringMap.existsUnique_continuousMap_lifts_of_range_leproof · cited by 0